报告人：Professor Martin Stynes

Beijing Computational Science Research Center

题目：Alikhanov's high-order scheme on fitted meshes for time-fractional initial-value problems and initial-boundary-value problems

时间：2018年5月24日上午10:00

地点：海韵行政楼B313

摘要：Alikhanov's high-order scheme for Caputo fractional derivatives of order $\alpha\in (0,1)$ is generalised to nonuniform meshes and analysed for initial-value problems (IVPs) and initial-boundary value problems (IBVPs) whose solutions display a typical weak singularity at the initial time. It is shown that, when the mesh is chosen suitably, the scheme attains order $3-\alpha$ convergence for the 1-dimensional IVP and second-order convergence for the IBVP. For the IBVP we consider the case where the spatial domain is the unit square and use a spectral method to discretise in space, but other spatial domains and other spatial dimensions and discretisations are possible. Numerical results demonstrate the sharpness of the theoretical convergence estimates.
This is joint work with Hu Chen (陈虎) of Beijing CSRC.

联系人: 许传炬教授

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